3E 


E 

O 


• 


Piezo- Electric  Activity  of  Rochelle 
Salt  Under  Various  Conditions 


BY 


J.  VALASEK 


A  THESIS 

SUBMITTED  TO  THE  FACULTY  OF  THE  GRADUATE  SCHOOL  OF  THE  UNIVERSITY 

OF  MINNESOTA  IN  PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS 

FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY. 


Reprinted  from  PHYSICAL  REVIEW,  Vol.  XIX.  X<>.  5 


Piezo- Electric  Activity  of  Rochelle 
Salt  Under  Various  Conditions 


BY 

J.  VALASEK 


A  THESIS 

SUBMITTED  TO  THE  FACULTY  OF  THE  GRADUATE  SCHOOL  OF  THE  UNIVERSITY 

OF  MINNESOTA  IN  PARTIAL  FULFILLMENT  OF  THE  REQUIREMENTS 

FOR  THE  DEGREE  OF  DOCTOR  OF  PHILOSOPHY. 


Reprinted  from  PHYSICAL  REVIEW,  Vol.  XIX,  No.  5,  May,  1922, 


•   •- 


. 


PIEZO-ELECTRIC   ACTIVITY   OF    ROCHELLE   SALT    UNDER 
VARIOUS    CONDITIONS. 

BY  J.  VALASEK. 

SYNOPSIS. 

Electrical  Properties  of  Rochelle  Salt  Crystal  are  analogous  to  the  magnetic  prop- 
erties of  iron,  the  dielectric  displacement  D  and  polarization  P  varying  with  the 
electric  field  E  in  the  same  general  manner  as  B  and  /  vary  with  H  for  iron,  and 
showing  an  electric  hysteresis  with  loops  distorted  by  an  amount  corresponding  to 
the  permanent  polarization  Po,  whose  value  is  about  30  e.s.u./cm.3  but  varies  for 
different  crystals.  The  dielectric  constant  (K  =  dD/dE)  was  measured  from  —  70° 
to  30°  C.  and  found  to  be  surprisingly  large,  increasing  from  about  50  at  —  70°  to  a 
maximum  of  about  1,000  near  o°.  The  modulus  of  piezo-electric  activity  for  shearing 
stresses  (5)  varies  with  temperature,  —  70°  to  40°  C.,  in  a  very  similar  manner,  increas- 
ing from  less  than  io~6  at  —  70°  to  a  maximum  of  about  io~4  at  o°.  The  ratio 
d/K  varied  with  the  electrode  material,  being  greater  for  tin  foil  than  for  mercury  elec- 
trodes. The  difference  may  be  due  to  the  alcohol  used  in  shellacking  the  tin-foil  elec- 
trodes on.  There  are  other  indications  that  5  and  K  are  related.  The  variation  of 
8  with  humidity  is  such  as  can  be  accounted  for  by  the  decrease  in  the  dielectric  con- 
stant of  the  outer  layer  as  a  result  of  dehydration.  The  change  of  polarization 
produced  by  pressure  as  measured  by  the  change  in  the  hysteresis  loop  agrees  with  the 
value  found  directly  from  the  piezo-electric  response,  as  required  by  Lord  Kelvin's 
theory.  Also  fatigue  effects  on  5  produced  by  temporarily  applied  fields  are  traceable 
to  fatigue  in  the  polarization.  The  electrical  conductivity  below  45°  is  less  than 
5  X  io~9  mhos/cm.3  but  from  43°  to  57°  increases  rapidly  to  5  X  io~4. 

Optical  Properties  of  Rochelle  Salt  as  Calculated  from  the  Natural  Polarization. — 
Assuming  only  one  electron  is  displaced  the  natural  period  corresponds  to  a  wave- 
length of  4.2  n  and  the  specific  rotation  for  sodium  light  comes  out  10°,  the  observed 
value  being  22°.!. 

T3  ECENTLY1  the  writer  described  some  experiments  on  the  dielectric 
A  V  and  piezo-electric  properties  of  Rochelle  salt,  which  were  made 
for  the  purpose  of  correlating  and  explaining  the  effects  observed  chiefly 
by  Cady  and  by  Anderson.  The  plates  used  were  cut  wrth  faces  per- 
pendicular to  the  3.  axis  and  with  edges  at  45°  with  the  b  and  c  axes. 
The  present  paper  is  a  continuation  of  the  work,  the  variations  in  the 
electrical  properties  having  been  studied  more  extensively.  The  appa- 
ratus and  method  of  observation  have  been  already  described  in  the  paper 
referred  to  above.  The  more  important  results  obtained  at  that  time 
can  be  summarized  as  follows: 

In  the  case  of  Rochelle  salt  the  dielectric  displacement  D,  electric 
intensity  £,  and  polarization  P  behave  in  a  manner  analogous  to  B, 
H,  and  /  in  the  case  of  magnetism.  Rochelle  salt  shows  an  electric 

1  J.  Valasek,  PHYS.  REV.  (2),  XVII,  p.  475. 


478648 


479 


J.    VALASEK. 


("SECOND 

[SERIES. 


hysteresis  in  P  analogous  to  the  magnetic  hysteresis  in  the  case  of  iron, 
the  loops  however  being  distorted  by  an  amount  corresponding  to  the 
permanent  polaiization  of  the  crystal  in  the  natural  state.  This  point 
of  view  is  very  effective  in  accounting  for  many  of  the  peculiarities 
observed. 

In  an  electric  field  the  piezo-electric  activity  has  a  maximum  for  a 
definite  value  of  the  field  and  decreases  to  a  small  value  in  both  directions. 
The  position  of  the  maximum  corresponds  to  the  greatest  rate  of  change 
of  polarization  with  electric  field  in  the  case  of  the  condenser  experiments. 
In  fact  if  force  and  electric  field  are  equivalent  in  changing  the  piezo- 
electric polarization  then  the  response  for  a  given  force  in  various  applied 
fields  must  necessarily  give  curves  of  the  same  general  nature  as  curves 
of  dP/dE  or  dD/dE  against  E.  It  is  permissible  to  interchange  D  and 
P  in  most  cases  because  of  the  large  dielectric  constant  of  Rochelle  salt. 

RELATION  BETWEEN  POLARIZATION  AND  PIEZO-ELECTRIC  ACTIVITY. 

The  activity  of  a  piezo-electric  crystal  is  intimately  related  to  the 
natural  polarization.  According  to  Lord  Kelvin  this  natural  moment 
is  masked  by  surface  charges  so  that  the  crystal  appears  to  be  uncharged. 
This  polarization  or  piezo-electric  moment  can  be  measured  independ- 
ently of  the  charges  on  the  electrodes,  through  the  distortion  of  the 
hysteresis  loop.  The  center  A  of  the  loop  is  found  by  a  consideration  of 
symmetry  and  may  be  assumed  to  represent  the  condition  of  no  polariza- 
tion. If  the  natural  condition  of  polarization  is  assumed  to  be  half  way 
between  the  two  branches  of  the  loop  at  zero  field  then  the  value  of  the 
permanent  polarization  P0  is  proportional  to  AB,  Fig.  i.  There  being 


60        60        100 

VOLTS 


.  1. 


no  field  applied,  the  equation  for  the  work  done  per  unit  charge  carried 
through  the  condenser  is: 


VoL.^XIX.J        P2EZO-ELECTRIC  ACTIVITY   OF   ROCHELLE   SALTS.  480 

SO  that 


where  Q0  is  the  apparent  average  permanent  charge  at  zero  field  given  by 
AB  (Fig.  i)  and  where  5  is  the  area  of  the  plate.  Calculation  gives  the 
value:  30  e.s.v./cm2. 

According  to  Lord  Kelvin's  theory  an  applied  stress  will  change  this 
polarization  so  as  to  create  free  charges  on  the  electrodes.  A  force  of 
250  grams  applied  to  the  crystal  should  consequently  shift  the  loop  by  an 
amount  equivalent  to  the  piezo-electric  response  for  250  grams.  When 
this  experiment  was  performed  another,  but  more  unsymmetrical  loop, 
was  obtained.  The  change  in  polarization  by  the  loop  method  was 
114  e.s.u./cm.2  while  the  piezo-electric  response  amounted  to  121 
e.s.u./cm.2 

The  value  of  P0  obtained  from  the  hysteresis  loops  is  only  approximate 
because  of  the  assumptions  involved  in  its  determination.  It  cannot, 
moreover,  be  fixed  definitely  enough  \.o  be  put  down  as  a  physical  constant 
of  Rochelle  salt  because  it  varies  with  different  specimens,  besides  chang- 
ing with  temperature,  pressure  and  fatigue.  The  value  P0  =  30  e.s.u./cm.2 
is  thought  to  be  a  representative  value  and  is  checked  by  other 
measurements.  The  writer  would  not  be  surprised,  however,  to  find 
other  specimens  giving  several  times  this  value.  The  change  in  polariza- 
tion due  to  pressure  however  is  derived  by  a  differential  method  eliminat- 
ing much  of  the  uncertainty  in  measurements  on  one  loop.  The  result 
in  this  case  should  be  fairly  definite,  as  indeed  it  seems  to  be. 

Piezo-electric  activity  depends  on  both  the  crystalline  structure  and 
on  the  polarization.  It  is  greatest  for  a  polarization  somewhat  larger 
than  normal  and  decreases  in  both  directions  for  changes  in  this  quantity, 
the  polarization  being  changed  by  applying  an  electric  field.  It  has  been 
shown  by  the  writer  that  this  relation  between  activity  and  applied 
field  is  approximately  like  that  of  the  derivative  dD/dE  of  the  curve 
relating  the  dielectric  displacement  D  and  the  electric  field  E  of  the 
crystal  used  as  a  condenser.  Since  this  latter  relation  is  in  the  form  of  a 
hysteresis  loop  it  follows  that  the  activity  is  also  a  double-  valued  function 
of  the  applied  field  depending  on  the  direction  of  variation  of  the  field. 
A  curve  illustrating  this  effect  is  reproduced  in  Fig.  2.  The  readings 
were  taken  in  as  short  a  time  as  possible  to  eliminate  fatigue.  These 
curves  show  that  the  piezo-electric  response  at  zero  field  depends  on  the 
previous  electrical  treatment  of  the  crystal.  The  latter  fact  has  also 
been  noted  by  W.  G.  Cady  in  the  report  previously  referred  to. 


48 1 


J.    VALASEK. 


[SECOND 

[SERIES. 


This  after-effect  does  not  persist  very  long  but  dies  off  exponentially 
with  the  time.  The  piezo-electric  response  or  ballistic  throw  of  the 
galvanometer  for  250  grams  has  been  observed  to  return  to  half  value  in 
I  minute  and  to  normal  in  over  20  minutes  after  fields  of  150  volts  have 
been  applied  for  3  minutes  previously.  There  is  a  much  greater  after- 
effect in  the  direction  of  increased  activity. 


!* 

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* 

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j- 

o  1 

'/\ 

/ 

3 

i 

/ 

£ 

\ 

/ 

/ 

\\ 

// 

i 

^ 

2 

^ 

^ 

^^_ 

—  jo-*" 

^ 

/ 

/20      -90      -60       -JO        O       JO         60       &O       UO 

2. 


Fig.  2. 

A  corresponding  dielectric  effect  is  indicated  by  the  double  value  of  the 
condenser  charge  at  zero  field  in  the  hysteresis  loops.  This  is  clearly 
due  to  a  fatigue  in  the  polarization  and  it  also  dies  off  exponentially  with 
time.  Herein  is  probably  found  the  explanation  of  the  "storage  battery 
effect"  described  by  W.  G.  Cady  who  observed  that  after  applying  a 
field  of  100  volts  for  some  time  there  was,  on  removal  of  the  field,  a  small 
current  which  decreased  gradually  and  flowed  from  the  crystal  as  from  a 
miniature  storage  battery. 

The  piezo-electric  fatigue  may  well  be  a  direct  result  of  the  fatigue  in 
the  polarization,  as  there  seems  to  be  a  close  relation  between  piezo- 
electric activity  and  polarization.  It  appears  that  the  activity  is  approxi- 
mately proportional  to  the  rate  of  change  of  polarization  with  applied 
field  and  hence  proportional  to  the  dielectric  constant.  An  examination 
of  the  temperature  variation  of  the  two  quantities  leads  to  this  conclusion. 
It  is  further  confirmed  as  regards  field  variation  by  the  fact  that  the 
relation  of  activity  to  applied  field  is  like  dD/dE  vs.  E  where  dD/dE  is 
merely  the  instantaneous  value  of  the  dielectric  constant  K.  As  an 
approximation  we  can  write  the  piezo-electric  modulus  8  proportional 
to  K: 


d  =  A-K. 


VOL.  XIX. 
No.  5. 


]        PIEZO-ELECTRIC  ACTIVITY   OF   ROCHELLE   SALTS. 


482 


If  this  equation  were  exact  A  would  be  a  fundamental  piezo-electric 
constant  of  the  substance,  being  of  the  order  of  I  X  io~7  between  —  20° 
C.  and  +  20°  C.  At  some  temperatures  and  for  some  exceptional 
specimens  the  relation  does  not  seem  to  be  so  simple. 

EFFECT  OF  MOISTURE  ON  PIEZO-ELECTRIC  PROPERTIES. 
In  order  to  investigate  the  effect  of  dryness  on  the  activity  of  Rochelle 
salt,  some  phosphorus  pentoxide  was  enclosed  in  the  chamber  containing 
the  crystal.  The  crystal  soon  started  to  dehydrate  and  after  a  few  days 
was  covered  by  a  white  coating.  The  piezo-electric  throw  for  a  load  of 
250  grams  continually  diminished.  When  the  response  was  tested  at 
different  fields  a  more  interesting  fact  was  observed.  Besides  the  de- 
crease in  response,  the  maxima  were  displaced  along  the  field  axis  into  a 
condition  of  greater  polarization.  This  is  shown  by  Fig.  3,  the  curves 


"200  -160    -120      -60     -40       O        40      30 

TlGURf  S, 
EFFECT  Or  DffYING 

Fig.  3. 


IZO      160     ZOO    )/OLTS 


being  taken  after  the  lapse  of  the  following  times:   (b)   I  day,  (c)  3  days, 
(d)   12  days. 

The  decrease  in  the  maxima  and  also  their  displacement  is  in  the  same 
direction  as,  and  may  be  entirely  due  to,  the  effect  of  different  dielectric 
properties  of  the  crystal  and  of  the  dehydrated  layer.  In  other  words 
the  presence  of  a  layer  of  inactive  dielectric  of  relatively  low  specific 
inductive  capacity  will  diminish  the  charge  on  the  plates  due  to  the 
polarization  of  the  central  active  layer,  and  thus  decrease  the  piezo- 
electric response.  It  will  also  diminish  the  effective  field  across  the 
active  layer  making  it  necessary  to  increase  the  potential  difference 


J.    VALASEK. 


[SECOND 

[SERIES. 


between  the  plates  to  produce  'the  same  field  across  the  inner  layer,  thus 
shifting  the  position  of  maximum  activity.  The  effects  due  to  uniform 
layers  can  be  readily  calculated.  Let  P0  be  the  polarization  produced  in 
the  middle  layer  by  pressure,  let  PI  and  PI  be  the 
electrically  induced  polarizations  in  the  dielectrics 
I  and  2  respectively  (Fig.  4).  Since  the  dielectric 
displacement  is  solenoidalwe  have: 


D'  =  E!  +  47rPi -f 
Since 

we  can  write 

D'  = 


o  =  E2  +  47rP2  =  47r<7. 


and 


X* 


— d 

Fig.  4. 


The  difference  of  potential  between  the  plates  is  zero  so  that,  replacing 
PO  by  (TO  : 

0  =  E2(d  -  ./)  +  Erf 


giving : 


•-+3* 

TO      Q 


—    KI)    +    Kid 


This  gives  us  a  relation  between  the  piezo-electric  response  at  zero  field 
of  the  crystal  with  the  dry  shell  and  of  the  same  crystal  before  it  dried. 
The  assumption  is  made  that  the  elasticity  of  the  shell  is  equal  to  that 
of  the  crystal  so  that  a  given  total  force  produces  the  same  polarization 
in  the  crystalline  portion. 

The  position  of  the  maximum  will  be  changed  to  another  value  of  total 
potential  difference  on  the  crystal.  Let  V  be  the  total  potential  drop 
and  V  be  the  drop  across  the  crystalline  part.  When  there  is  no  de- 
hydrated layer  present 

V  =  V  =  dE, 

where  E  is  the  field  strength  in  the  dielectric.  When  there  is  a  layer  of 
uniform  thickness  (d  —  J)/2  on  both  faces  then 


V  =  (d  - 


+  tE', 


where  E"  and  Ef  are  the  field  strengths  in  the  dielectrics  2  and  I  respec- 
tively.    The  dielectric  displacement 


D 


KlE' 


VoL.^XIX.j        PIEZO-ELECTRIC  ACTIVITY   OF   ROCHELLE   SALTS.  484 

is  solenoidal,  and  we  can  eliminate  E"  from  equations  above  and  write: 
V'  =  dE  =  (d  -  t)  -1  E'  +  tEf  +  47rP0 


Since  the  last  term  is  small  compared  to  the  rest  of  the  expression,  this 
gives  : 


E       t(K2-  KI)  +  <f«i- 

The  following  quantities  were  measured  and  substituted  in  these  equa- 
tions. 

KI  =  looo,         d  =  0.22  cm., 

K2  =     180,          t  —  0.14. 

The  quantity  t  is  an  average  obtained  by  breaking  the  crystal  in  several 
places  and  it  is  probably  not  very  accurate  because  of  the  irregularity 
of  the  outer  layer.  We  should,  however,  get  a  rough  check  on  the 
plausibility  of  the  proposed  explanation.  We  find  that 


and  that 


While  the  values  of  Q'/Q  and  E'/E  from  the  maxima  of  curves  a  and  d 
of  Fig.  3  are  respectively  0.39  and  0.33.  The  agreement  is  not  as  good 
as  could  be  desired  even  after  making  allowance  for  the  difficulties  in 
estimating  t.  Possibly  there  is  a  true  humidity  effect  with  respect  to 
piezo-electric  activity  but  the  above  shows,  at  least,  that  it  is  quite  small. 

PIEZO-ELECTRIC  ACTIVITY  AND  TEMPERATURE. 

In  order  to  investigate  the  variation  of  activity  with  temperature,  the 
chamber  holding  the  crystal  was  immersed  in  CO2  snow.  After  every- 
thing was  thoroughly  cooled  and  at  —  75°  C.,  the  chamber  was  allowed 
to  heat  up.  Above  —  35°  C.  an  electric  heater  was  used.  It  was  wound 
on  a  glass  jar  and  insulated  from  the  crystal  chamber  by  a  felt  jacket. 
This  jar  was  immersed  in  an  oil  bath  to  steady  the  heating  rate  while  the 
felt  eliminated  any  rapid  changes  of  heating  of  the  crystal.  The  current 
was  gradually  increased  so  as  to  keep  the  rate  of  heating  uniformly  between 
|°  and  i°  C.  per  minute  so  as  to  eliminate  thermoelastic  stresses.  The 
temperature  was  measured  by  means  of  a  copper-constantan  thermo- 
couple directly  soldered  to  an  electrode  on  the  crystal.  In  this  way  the 
actual  temperature  of  the  crystal  itself  was  measured. 


J.    VALASEK. 


[SECOND 

[SERIES. 


When  the  piezo-electric  response  or  galvanometer  throw  for  250  grams 
was  measured  at  the  various  temperatures  for  the  first  specimen  the 
curve  of  Fig.  5  was  obtained.  This  was  duplicated  to  check  the  second 


-6o   -so    -to    -30    -zo    -/o 

Pl£ZO£L£CTJ?lC 


/o      20     Jo     4o 

»  TFffffffA  TURC 


Fig.  5. 

maximum.  At  —  70°  C.  the  piezo-electric  activity  is  comparatively 
negligible.  As  the  temperature  is  raised  slowly  the  activity  stays  small 
until  —  30°  C.  is  reached.  At  —  20°  C.  it  is  rising  very  rapidly,  reaching 
a  maximum  at  about  o°  C.  It  decreases  again  but  at  23°  C.  comes  to  a 
small  but  sharp  maximum  from  which  it  diminishes  slowly,  becoming  very 
small  at  +  50°  C.  The  magnitude  of  the  second  maximum  varies  with 
the  temperature  at  which  heating  begins.  This,  second  maximum  was 
found  in  the  case  of  two  crystal  plates  provided  with  tinfoil  electrodes 
attached  by  shellac. 

Three  other  crystals  were  prepared  with  electrodes  of  mercury  held 
against  the  crystal  by  two  rectangular  cups  attached  by  wax.  The 
thermocouple  wires  were  immersed  in  the  mercury.  None  of  the  crystals 
so  prepared  gave  the  second  maximum.  Moreover,  none  of  them  were 
as  active  as  those  used  above.  The  variation  of  piezo-electric  response 
of  these  specimens  is  shown  in  Fig.  6.  The  increase  at  —  30°  to  —  15°  C. 
and  the  decrease  at  +20°  C.  to  +  30°  C.  are  remarkably  consistent. 
Between  —  15°  and  +  20°  C.,  however,  they  each  show  different  char- 
acteristics. These  mercury  electrode  crystals  seemed  to  give  more  con- 
stant results  than  the  crystals  with  tinfoil  electrodes  attached  by  shellac. 

It  was  then  suspected  that  the  increased  response  of  the  crystal  with 


VOL.  XIX. 
No.  5. 


]        PIEZO-ELECTRIC  ACTIVITY   OF   ROCHELLE   SALTS. 


486 


-70 


•to 


0          /O         ZO         JO 
\ 

-  SA*erir&T/i£#r 


Fig.  6. 


tin  foil[  electrodes  and  the  presence  of  the  second  maximum  was  in  some 
way  due  to  the  penetration  into  the  crystal  of  the  alcohol  solvent  of 
shellac.  Accordingly  one  of  the  crystals  originally  with  mercury  elec- 
trodes[was  provided  with  the  other  type.  As  soon  as  the  shellac  was 
sufficiently  dry,  Curve  b,  Fig.  7  was  obtained,  the  response  originally 


Fig.  7. 

having  followed  Curve  a.  The  sensitivity  increased  seven-fold  at  some 
temperatures  but  there  was  no  second  maximum.  In  two  weeks  the 
characteristics  had  changed  to  those  shown  in  Curve  c,  seemingly  checking 
the  suspicion  that  alcohol  was  responsible  for  the  second  maximum  and 
for  the  increased  sensitivity.  It  would  be  interesting  to  use  alcohol  cup 
electrodes  and  investigate  the  continuous  effect  of  alcohol  soaking  into 
the  crystal.  Tlie  effect  is  probably  not  chemical. 


J-    VALASEK. 

In  a  paper  on  the  piezo-electric  effect  on  Rochelle  salt/A.  M.  Nicolson1 
describes  a  method  for  desiccating  the  crystals  by  soaking  in  alcohol  and 
heating,  thus  making  them  stronger  and  more  sensitive.  'The  writer  is 
certain,  from  his  work  on  the  subject,  that  complete  desiccation  will  make 
the  crystal  entirely  inactive.  In  the  above  method,  apparently,  the 
treatment  is  not  prolonged  enough  to  completely  dehydrate  more  than 
a  shell  around  the  crystal  and  its  effectiveness  may  be  connected  with 
the  penetration  of  the  alcohol  into  the  crystal.  The  heating  at  40°  C. 
may  also  be  effective  in  allowing  a  rearrangement  and  recrystallization 
of  some  of  the  molecules  or  groups  not  properly  oriented.  W.  G.  Cady, 
as  well  as  the  writer,  has  observed  that  heating  the  crystal  will  usually 
increase  its  sensitivity  permanently,  although  sometimes  the  reverse 
is  true. 

An  interesting  side-light  on  the  temperature  variation  of  piezo-electric 
activity  is  offered  by  a  study  of  curves  like  that  of  Fig.  2  but  at  different 
temperatures.  They  show  that  the  effect  of  temperature  is  not  so  much 
to  change  the  piezo-electric  activity  as  to  shift  the  position  of  the  maxi- 
mum from  one  value  of  the  field  to  another.  This  is  probably  connected 
with  the  variation  of  the  dielectric  constant  with  temperature  which 
will  be  taken  up  presently. 

The  charging  throws  of  the  crystal  used  as  a  condenser  show  variations 
similar  to  those  of  the  activity  except  that  they  do  not  tend  to  zero  but  to 
a  constant  value  at  the  lower  temperatures.  The  crystals  giving  the 
second  maximum  on  the  piezo-electric  curve  show  a  similar  peculiarity 
here.  The  crystals  with  the  mercury  electrodes  give  more  regular  curves. 
At  20°  to  25°  C.  the  crystals  of  both  types  begin  to  conduct,  causing  a 
steady  drift  of  the  galvanometer.  Experiments  seem  to  indicate  that 
Ohm's  law  holds  at  least  approximately.  The  conduction  was  at  first 
thought  to  be  electrolytic  because  of  the  manner  in  which  Rochelle  salt 
melts.  Instead  of  real  melting  it  appears  that  the  crystal  dissolves  in 
its  water  of  crystallization  which  is  set  free  at  55°  C.  The  desiccated 
crystal,  however,  decomposes  into  a  tarry  product  and  emits  heavy  white 
fumes  above  150°  C.,  without  melting.  The  dehydrated  crystal  also 
begins  to  conduct  above  20°  C.,  making  it  probable  that  electronic  and 
not  electrolytic  conduction  is  observed. 

Measurements  of  conductivity  were  made  on  the  natural  crystal  at 
various  temperatures  up  to  its  liquefying  point.  The  values  obtained 
after  the  conductivity  was  sufficiently  large  to  use  a  Wheatstone  bridge 
are  as  follows : 

1  A.  M.  Nicolson,  Proc.  Am.  Inst.  Ele.  Eng.,  Vol.  38,  p.  1315  (1919). 


VOL.  XIX.' 
No.  5. 


PIEZO-ELECTRIC  ACTIVITY  OF   ROCHELLE   SALTS. 


488 


TABLE  I. 

Temperature.  Conductivity. 

Less  than  43°  C Less  than  0.5  X  l-0-»  mhos/cm3. 

43  0.5  X  1C-8 

45  1.0  X  10-8 

47  . .  0.3  X  10-7 

49  0.5  X  10-7 

51    ,  0.5  X  10-6  • 

53  0.6  X  10~4 

54  1.7  X  10-< 

57  5.0  X  10-4 

Greater  than  57         1 5.0  X  10'4 

At  temperatures  below  20°  the  dry  crystal  is  a  fairly  good  insulator 
having  a  specific  conductivity  of  5  X  io~12  mhos/cm.3  at  o°  C.  The 
conductivity  decreases  slightly  at  still  lower  temperatures.  In  all  these 
measurements  the  surfaces  were  thoroughly  dried  by  the  presence  of 
phosphorus  pentoxide  in  the  crystal  chamber. 

TABLE  II. 


Temp. 
Cent. 

Dielectric  Constant. 

Piezoelectric  Modulus. 

A 

B 

A 

B 

—  70 

71 
85 
140 
386 
943 
1,380 
1,100 
688 
423 
Conduction 

42 
50 
146 
252 
924 
956 
928 
645 
146 
commences 

0.041  X  10~5 
0.068       " 
0.41 
5.4 
18.9 
22.9 
18.9 
13.5 
2.2 
0.41 

0.017  X  10~5 
0.017      " 
0.065       " 
1.08 
6.07 
6.75 
7.42 
8.10 
1.08 
0.41 

-50  
-30                .     . 

-20  

—  10     

0  
10  
20 

30 

Table  II.  gives  values  of  the  dielectric  constants  for  a  field  changing 
from  o  to  880  volts/cm,  and  of  the  piezo-electric  modulus  5u  for  shearing 
stresses  of  220  grams/cm.2.  The  modulus  614  is  defined  by  the  relation 
given  by  Voigt  en  =  —  S^F,  where  <TI  is  the  surface  density  of  charge 
and  Fz  is  the  shearing  stress  producing  it.  The  given  values  are  thought 
to  be  the  most  representative  in  each  case.  They  are  subdivided  into 
two  classes,  according  to  whether  the  electrodes  were  tinfoil  attached 
by  shellac  (column  A)  or  mercury  in  direct  contact  with  the  crystal 
(column  B).  The  former  method  is  the  most  convenient  to  use  in 
general  practice,  but  the  latter  is  thought  to  give  more  exactly  the  prop- 
erties of  Rochelle  salt  in  the  direction  of  the  a  axis.  The  dielectric 


489 


VALASEK. 


constants  are  surprisingly  large,  a  fact  noticed  by  Pockels1  who  supposes 
that  this  is  due  to  "internal  conductivity."  The  writer  however  has 
measured  separately  the  conductivity  at  these  temperatures  and  is  of 
the  opinion  that  this  is  a  true  dielectric  constant  arising  from  polarization 
of  the  dielectric,  and  for  this  reason  being  so  closely  related  to  the  piezo- 
electric effect.  Because  of  the  relatively  low  specific  inductive  capacity 
of  the  desiccated  crystal  it  is  thought  that  the  high  specific  inductive 
capacity  of  Rochelle  salt  is  partly  due  to  the  water  molecule. 

MAGNETIC  ANALOGY. 

There  seems  to  be  a  strong  analogy  between  the  behavior  of  Rochelle 
salt  as  a  dielectric  possessing  hysteresis  and  having  an  exceptionally 
large  dielectric  constant,  and  the  phenomena  of  ferromagnetism.  Ac- 
cordingly some  of  the  features  of  Weiss's  theory  of  magnetism  may  find 
their  counterpart  in  the  phenomena  in  Rochelle  salt.  Weiss2  plots  the 
susceptibility  against  the  reciprocal  of  the  absolute  temperature  and  finds 
that  the  curve  may  be  represented  by  a  succession  of  straight  lines.  He 
interprets  the  sudden  changes  in  slope  as  due  to  changes  in  the  number 
of  magnetons.  If  the  data  of  Figs.  8a  and  12  are  plotted  against  the 
reciprocal  of  the  absolute  temperature  one  likewise  gets  what  may  be 
considered  to  be  a  succession  of  straight  lines.  Actually  however  there 
occur  rounded  corners  where  the  curves  suddenly  change  direction. 
This  may  be  due  to  slight  non-uniformity  in  heating  which  occurred  in 
spite  of  the  precautions  taken.  It  is  considered  that  the  straight  portions 
are  at  least  as  definite  as  those  shown  in  Weiss's  paper.  The  most  abrupt 
changes  are  at  —  20°  C.  and  at  +20°  C.  These  may  accordingly  be 
considered  as  the  "Curie  points"  in  Rochelle  salt. 

RELATION  TO  OPTICAL  PROPERTIES. 

Some  of  the  optical  properties  of  Rochelle  salt  can  be  at  least  approxi- 
mately found  from  the  electrical  data  given.  In  the  course  of  this 
calculation  it  is  of  course  necessary  to  introduce  some  assumptions  notably 
as  to  the  nature  of  the  permanent  polarization.  If  one  knew  just  how  the 
permanent  polarization  was  pioduced  he  could  find  the  free  period  of  this 
mechanism.  The  data  needed  are  the  force  per  unit  displacement  / 
and  the  mass  m  of  that  part  of  the  molecule.  The  wave-length  corre- 
sponding to  the  free  period  is  given  by  the  expression 

X    =    271 

c  being  the  velocity  of  light. 

1  Pockels,  Lehrbuch  der  Krystaloptik,  p.  508. 

2  P.  Weiss,  J.  de  Physique,  Vol.  i,  p.  968  (1911). 


NoL'5XIX']         PIEZO-ELECTRIC   ACTIVITY   OF    ROCHELLE    SALTS.  490 

Let  us  assume  for  simplicity  that  only  one  electron  is  involved  in  the 
creation  of  the  permanent  moment.  The  quantity  /  can  be  derived  from 
the  value  of  the  permanent  moment  PQ  =  30  e.s.u./cm.2  and  from  the 
displacement  of  the  electron  producing  it.  Since  the  force  on  an  electron 
inside  a  dielectiic  of  polarization  P0  is  roughly  equal  to  fPo^1  the  expres- 
sion for  the  wave-length  may  be  put  in  the  form  : 


The  value  of  d,  the  displacement  of  the  electron,  can  be  found  as  follows: 
Taking  30  e.s.u./cm.2  as  the  natural  polarization,  the  moment  per 
molecule  is  obtained  by  dividing  by  the  number  of  molecules  per  c.c., 
the  result  being  7.1  X  io~21  e.s.u.  In  each  of  these  molecules  there  are 
140  electrons,  this  being  the  sum  of  the  atomic  numbers  of  the  constituent 
elements  in  Rochelle  salt.  If  we  suppose  as  above  that  only  one  of  these 
is  effective  in  producing  the  piezo-electric  moment,  its  displacement  from 
the  center  of  force  of  the  rest  of  the  molecule  will  be  d  =  2.7  X  io~n  cm. 
It  would  of  course  be  more  reasonable  to  suppose  that  at  least  several 
of  the  electrons  are  displaced  by  different  amounts,  and  to  the  extent 
that  we  do  this  the  value  calculated  above  becomes  smaller. 

Using  these  values  of  P0  and  d  for  the  simple  case  treated  above  we 
find  for  the  wave-length  the  Value: 

X  =  4.2  p. 

Coblentz2  shows  the  presence  of  fairly  strong  absorption  in  this  region  of 
the  infra-red.  This  may,  however,  be  due  to  the  water  of  crystallization 
and  not  to  the  cause  cited  above.  These  two  possibilities  should  be  dis- 
tinguishable experimentally  because  the  character  of  the  absorption  due 
to  these  electrons  should  change  greatly  with  the  temperature,  as  the 
piezo-electric  elasticity  or  force  per  unit  displacement  of  the  electrons 
changes. 

The  natural  period  as  found  above  should  be  the  same  as  that  involved 
in  rotatory  dispersion  formulae,  since  both  the  piezo-electric  effect  and 
optical  rotation  are  due  to  an  unsymmetrical  or  twisted  structure  of  the 
molecule.  J.  J.  Thomson3  gives  an  approximate  formula  for  the  specific 
rotation,  namely: 


1  H.  A.  Lorentz,  Theory  of  Electrons,  p.  306. 

-  W.  W.  Coblentz,  Infra  Red  Spectra,  Vol.  2,  p.  38. 

3J.  J.  Thomson,  Phil.  Mag.,  Dec.,  1920. 


491  J.    VALASEK. 

in  which  e  is  the  charge  of  the  electron,  c  is  the  velocity  of  light  and  M 
and  m  are  the  masses  of  the  molecule  and  of  the  electron,  d  is  the  radius 
of  the  molecule,  p  is  the  free  period,  and  n  is  the  frequency  for  which  p 
is  to  be  calculated.  Using  the  value  of  .p  derived  from  piezo-electric  data 
we  find  for  sodium  light  the  specific  rotation  of  the  order  of  magnitude  of 
10°,  the  tables  giving  22.1°.  Considering  the  fact  that  so  little  is  known 
of  the  structure  of  the  Rochelle  salt  molecule,  the  approximation  is  fair. 
The  writer  is  indebted  to  Professor  W.  F.  G.  Swann,  who  initiated  this 
research  and  gave  many  helpful  suggestions,  and  to  Dr.  W.  R.  Whitney, 
Director  of  the  Research  Laboratory  of  the  General  Electric  Company, 
whose  presentation  of  two  beautifql  crystals  made  the  work  possible. 

PHYSICAL  LABORATORY, 

UNIVERSITY  OF  MINNESOTA. 


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